Circular colorings of weighted graphs
Journal of Graph Theory
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Automatic storage optimization
SIGPLAN '79 Proceedings of the 1979 SIGPLAN symposium on Compiler construction
Heuristic methods for graph coloring problems
Proceedings of the 2005 ACM symposium on Applied computing
Journal of Artificial Intelligence Research
About equivalent interval colorings of weighted graphs
Discrete Applied Mathematics
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Given a graph G=(V,E) with strictly positive integer weights 驴 i on the vertices i驴V, an interval coloring of G is a function I that assigns an interval I(i) of 驴 i consecutive integers (called colors) to each vertex i驴V so that I(i)驴I(j)=驴 for all edges {i,j}驴E. The interval coloring problem is to determine an interval coloring that uses as few colors as possible. Assuming that a strictly positive integer weight 驴 ij is associated with each edge {i,j}驴E, a bandwidth coloring of G is a function c that assigns an integer (called a color) to each vertex i驴V so that |c(i)驴c(j)|驴驴 ij for all edges {i,j}驴E. The bandwidth coloring problem is to determine a bandwidth coloring with minimum difference between the largest and the smallest colors used. We prove that an optimal solution of the interval coloring problem can be obtained by solving a series of bandwidth coloring problems. Computational experiments demonstrate that such a reduction can help to solve larger instances or to obtain better upper bounds on the optimal solution value of the interval coloring problem.